STD 12 - 9. Ray optics abd optical instruments — NEET STD 11 Science — Question

Use the model described above to answer the following three questions for a particle moving in the line $x=0$ to $x=a$. Take $h=6.6 \times 10^{-34} \mathrm{~J} \mathrm{~s}$ and $e=1.6 \times 10^{-19} \mathrm{C}$.

$1.$ The allowed energy for the particle for a particular value of $n$ is proportional to

$(A)$ $a^{-2}$ $(B)$ $a^{-3 / 2}$ $(C)$ $a^{-1}$ $(D)$ $a^2$

$2.$ If the mass of the particle is $m=1.0 \times 10^{-30} \mathrm{~kg}$ and $a=6.6 \mathrm{~nm}$, the energy of the particle in its ground state is closest to

$(A)$ $0.8 \ \mathrm{meV}$ $(B)$ $8 \ \mathrm{meV}$ $(C)$ $80 \ \mathrm{meV}$ $(D)$ $800 \ \mathrm{meV}$

$3.$ The speed of the particle, that can take discrete values, is proportional to

$(A)$ $n^{-3 / 2}$ $(B)$ $n^{-1}$ $(C)$ $n^{1 / 2}$ $(D)$ $n$

Give the answer question $1, 2$ and $3.$

$(I)$ Photoelectrons are emitted as soon as the metal is exposed to light.

$(II)$ There is a minimum frequency below which no photo-current is observed.

$(III)$ The stopping potential is proportional to the frequency of light.

$(IV)$ The photo-current varies linearly with the intensity of the light.

Which of the above statements indicate that light consists of quanta (photons) with energy proportional to frequency?

Choose the correct answer from the options given below: